# -*- coding: utf-8 -*-
"""
Created on Sun Jun 16 20:13:42 2019

@author: Administrator
"""

"""

這個函數(shù)的作用是將一個矩陣給轉(zhuǎn)換成一個圖，
矩陣以多維列表的形式存在，即列表的列表
此處的轉(zhuǎn)換是針對無向圖

根據(jù)鄰接矩陣得到圖之后，我們就可以調(diào)用networkx
里面的各種函數(shù)來分析圖的性質(zhì)，比如度分布，
平均路徑程度，聚類系數(shù)等一系列圖的拓撲性質(zhì)

"""

import networkx as nx


def matrix_to_graph():

  G = nx.Graph()
  
  #matrix為鄰接矩陣，以多維列表的形式存在
  matrix = [[0, 1, 1],[1,0,1],[1,1,0]]
  
  nodes = range(len(matrix))
  G.add_nodes_from(nodes)
 
  for i in range(len(matrix)):
    for j in range(len(matrix)):
      if(matrix[i][j] == 1):
		G.add_edge(i, j)
        
  position = nx.circular_layout(G)
  nx.draw_networkx_nodes(G,position, nodelist=nodes, node_color="r")
  nx.draw_networkx_edges(G,position)
  nx.draw_networkx_labels(G,position)
  print(nx.to_numpy_matrix(G))

matrix_to_graph()

import networkx as nx ? #導入networkx包
import random?? ??? ??? ?#導入random包
import matplotlib.pyplot as plt #導入畫圖工具包

G = nx.Graph()?? ??? ??? ?#建立無向圖
H = nx.path_graph(100)?? ?#添加節(jié)點
G.add_nodes_from(H)?? ??? ?#添加節(jié)點

def rand_edge(vi,vj,p=0.2):?? ??? ?#默認概率p=0.1
? ? probability =random.random()#生成隨機小數(shù)
? ? if(probability<p):?? ??? ??? ?#如果小于p
? ? ? ? G.add_edge(vi,vj) ??? ??? ?#連接vi和vj節(jié)點

i=0
while (i<100):
? ? j=0
? ? while(j<i):
? ? ? ? ? ? rand_edge(i,j)?? ??? ?#調(diào)用rand_edge()
? ? ? ? ? ? j +=1
? ? i +=1

number_components = nx.number_connected_components(G)?
largest_components = max(nx.connected_components(G), key=len)
print("最大連通子圖:" + str(largest_components))
print("最大連通子圖長度："+ str(len(largest_components)))
print("連通子圖個數(shù): "+str(nx.number_connected_components(G)))

nx.degree(G)
DVweight = G.degree()
degree_sum = sum(span for n, span in DVweight) ?? ??? ?#各節(jié)點度數(shù)之和
degree_max = max(span for n, span in DVweight)?? ??? ?#節(jié)點最大度數(shù)

import networkx as nx     #導入networkx包
import random			  #導入random包
import matplotlib.pyplot as plt

G = nx.Graph()
H = nx.path_graph(100)
G.add_nodes_from(H)

def rand_edge(vi,vj,p=0.2):
    probability =random.random()
    if(probability<p):
        G.add_edge(vi,vj)   
i=0
while (i<100):
    j=0
    while(j<i):
            rand_edge(i,j)
            j +=1
    i +=1

number_components = nx.number_connected_components(G) 
largest_components = max(nx.connected_components(G), key=len)
nx.degree(G)
DVweight = G.degree()
degree_sum = sum(span for n, span in DVweight) 		#各節(jié)點度數(shù)之和
degree_max = max(span for n, span in DVweight)		#節(jié)點最大度數(shù)

print("度數(shù)之和: " + str(degree_sum))
print("節(jié)點最大度數(shù)：" + str(degree_max))
print("最大連通子圖:" + str(largest_components))
print("最大連通子圖長度："+ str(len(largest_components)))
print("連通子圖個數(shù): "+str(nx.number_connected_components(G)))
nx.draw_networkx(G, with_labels=True)
plt.show()